Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M. a. T(6,2) M(2,0)
b. A(-4, 3) M(-1, -1)

The formula to find the mid-point of a line segment give the two end points is:

M

=

(

x

1

+

x

2

2

,

y

1

+

y

2

2

)

Where

M

is the midpoint and the given points are:

(

x

1

y

1

)

and

(

x

2

y

2

)

Substituting the information we have gives:

(

1.5

,

4.5

)

=

(

−

3.5

+

x

2

2

,

−

6

+

y

2

2

)

To find

x

2

we need to solve this equation:

1.5

=

−

3.5

+

x

2

2

2

×

1.5

=

2

×

−

3.5

+

x

2

2

3

=

2

×

−

3.5

+

x

2

2

3

=

−

3.5

+

x

2

3.5

+

3

=

3.5

−

3.5

+

x

2

6.5

=

0

+

x

2

6.5

=

x

2

x

2

=

6.5

To find

y

2

we need to solve this equation:

4.5

=

−

6

+

y

2

2

2

×

4.5

=

2

×

−

6

+

y

2

2

9

=

2

×

−

6

+

y

2

2

9

=

−

6

+

y

2

9

+

6

=

6

−

6

+

y

2

15

=

0

+

y

2

15

=

y

2

y

2

=

15

The other end point of the segment is:

(

6.5

,

15

)

d

step-by-step explanation:

d